Measuring motor activity in major depression: the association between the Hamilton Depression Rating Scale and actigraphy

Despite the use of actigraphy in depression research, the association of depression ratings and quantitative motor activity remains controversial. In addition, the impact of recurring episodes on motor activity is uncertain. In 76 medicated inpatients with major depression (27 with a first episode, 49 with recurrent episodes), continuous wrist actigraphy for 24h and scores on the Hamilton Depression Rating Scale (HAMD) were obtained. In addition, 10 subjects of the sample wore the actigraph over a period of 5 days, in order to assess the reliability of a 1-day measurement. Activity levels were stable over 5 consecutive days. Actigraphic parameters did not differ between patients with a first or a recurrent episode, and quantitative motor activity failed to correlate with the HAMD total score. However, of the motor-related single items of the HAMD, the item activities was associated with motor activity parameters, while the items agitation and retardation were not. Actigraphy is consistent with clinical observation for the item activities. Expert raters may not correctly rate the motor aspects of retardation and agitation in major depression.

Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Über Aus- und Rückwanderung : Vortrag, geh. am Mittwoch, 17. Sept. 1902 in d. Henry Jones-Loge in Hamburg

von Paul Laskar